Resolvent estimates for wave operators in Lipschitz domains

TL;DR

This paper investigates the resolvent of wave operators on Lipschitz domains, providing existence results and estimates for both real and complex cases under Dirichlet and Neumann boundary conditions.

Contribution

It offers new resolvent estimates for wave operators in Lipschitz domains, extending understanding to both real and complex spectral parameters.

Findings

Existence of resolvent operators in Lipschitz domains

Estimates for resolvent operators in real and complex cases

Applicability to Dirichlet and Neumann boundary conditions

Abstract

In this paper we study the resolvent of wave operators on open and bounded Lipschitz domains of $\mathbb{R}^N$ with Dirichlet or Neumann boundary conditions. We give results on existence and estimates of the resolvent for the real and complex cases.